Question #68801

Derive the conditions for steady state in Solow model in an economy. What is the significance of decreasing returns in the Solow model ?

Expert's answer

The Solow–Swan model is an exogenous growth model, an economic model of long-run economic growth set within the framework of neoclassical economics.

Steady-state in the Solow model: in long-run equilibrium, capital per worker (the capital-lab or ratio) is constant. Steady-state condition: the following equation defines a steady-state in the Solow model.

General case: s f(k_ss)=δk_ss→k_ss/f(k_ss)=s/δ

Cobb-Douglas case: sk_ss^α=δk_ss→k_ss=(s/δ)^(1/(1-α))

The key assumption of the neoclassical growth model is that capital is subject to diminishing returns in a closed economy.

Steady-state in the Solow model: in long-run equilibrium, capital per worker (the capital-lab or ratio) is constant. Steady-state condition: the following equation defines a steady-state in the Solow model.

General case: s f(k_ss)=δk_ss→k_ss/f(k_ss)=s/δ

Cobb-Douglas case: sk_ss^α=δk_ss→k_ss=(s/δ)^(1/(1-α))

The key assumption of the neoclassical growth model is that capital is subject to diminishing returns in a closed economy.

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